Tunnel Through Earth: Particle Motion Facts

[erisedk]

Homework Statement

A particle is dropped from a height equal to the radius of the Earth into a tunnel dug through the Earth along one of the diameters. Which of the following is/are true--
(A) Particle will oscillate through the Earth to a height R on both sides
(B) Particle will execute simple harmonic motion
(C) Motion of the particle is periodic
(D) Particle passes through the centre of Earth with a speed √ (2GM/R)

Homework Equations

The Attempt at a Solution

The answers are (A), (C), (D).

I know A and C will be true, A due to conservation of energy and C because such motions are almost always periodic, but I don't get why (B) is wrong and (D) is true.
Is (B) wrong because field above the Earth is GM/r^2 and inside the Earth GMr/R^3 and these are different, so it won't be SHM?
In any case, I can't prove (D) to be true (I tried energy conservation)

 

[erisedk]

Sorry, got it.

 

[Loren]

It will melt.